On old phone, do you have a file manager installed? If not, I like Astro File Manager. Once that is installed, open it and navigate to "manage my files". You should see a folder called DCIM. You pictures should be here. Long press on it, and choose "copy". Use the "up arrow" on Astro to go back a page. There you should see your SD card. Tap it. I like "order", so I would now use the "plus" sign in Astro to make a new folder. I would call it "old pictures" or something easy to remember. After folder is there, tap it. Then press "paste" from top of Astro choices...

You can also connect the old phone to a computer and choose to connect it as a drive to the PC and access the files that way.

One more thing: on the new phone, go into the camera app and verify the storage location of photos. On the Droid 3, when you start the camera app and it notices a new SD card, it offers to use that the first time that it is opened. If you choose not to, you can change later by hitting menu, then the "gear" icon, then change the storage location to the SD card. If your new phone has an SD card slot, I bet that the camera app has a similar setting.

If I can add one more thing, if you have Dropbox or Sugarsync, or use Google+, you can set up those apps on the new phone to automatically upload any new photos to those services as soon as the photos are taken.